Connections between cutting-pattern sequencing, VLSI design, and flexible machines

Abstract

The minimization of open stacks problem (MOSP) arises on the sequencing of a set of cutting patterns in order to minimize the maximum number of open stacks around the cutting saw. A previous study formulated the problem mathematically and raised a number of theoretical conjectures. In this work we deal with those conjectures. It is shown that the MOSP is NP-hard. A connection to the field of VLSI design, joining practitioners from both computer science and operations research, is established. Additional conjectures concerning the existence of simultaneous optimal solutions to related pattern-sequencing problems are also clarified. Scope and purpose There has been a recent surge in interest over industrial pattern-sequencing problems. The goal of these problems generally is to find a particular sequence of production patterns that minimizes production costs. An important pattern-sequencing problem arising in settings as distinct as in the sequencing of cutting stock and in factories employing flexible machines is known as the minimization of open stacks problem (MOSP). Though this problem has been recently analyzed in detail, its computational complexity remained an open question, as were some important conjectures relating it to other industrial problems, such as the minimization of order spread problem (MORP), the minimization of tool switches problem (MTSP), and the minimization of discontinuities problem (MDP). We deal with these questions, and, moreover, we show that the MOSP is deeply related to a problem in the field of VLSI layout, thus enabling a link between researchers in computer science and operations research.